Given observations \(Z_{1:k}\)  up to viewpoint \(k\) , our goal is to estimate the posterior distribution of the 6D object pose \(P\left(R_{wo}, t_{wo}|Z_{1:k}\right)\) . The direct computation of this distribution is generally not feasible since object translation \(t_{w,o}\)  and rotation \(R_{wo}\)  have distinct distributions. Specifically, the translation distribution \(P\left(t_{wo}\right)\)  is straightforward and expected to be unimodal. In contrast, the distribution for object rotation \(P\left(R_{wo}\right)\)  is less obvious due to complex uncertainties arising from shape symmetries, appearance ambiguities, and possible occlusions. Inspired by [1]}, we decompose the posterior \(P\left(R_{wo}, t_{wo}|Z_{1:k}\right)\)  into:
\(P\left(R_{wo}, t_{wo}|Z_{1:k}\right) = P\left(R_{wo}|Z_{1:k}, t_{wo}\right) P\left(t_{wo}|Z_{1:k}\right)\) 
